The attack, apparently targeting the US-led coalition force in the troubled southern city of Kandahar, was the eighth in Afghanistan in more than two months.
Police official Abdul Hakim said the the bomber was walking and detonated himself but missed the convoy, killing a passerby and wounding two others.
A spokesman for the US-led coalition, Colonel Jerry O'Hara, said: "Our initial report says that there was an IED strike in Kandahar city, involving coalition forces.
"One service member was cut right above the eye and treated on the scene," he said.
The deadliest in the latest series of suicide attacks in Afghanistan was in the capital, Kabul, on 14 November and targeted a Nato-led peacekeeping force.
A German soldier and eight civilians were killed and 15 other people wounded.
Another attack killed eight Afghan soldiers and a civilian driver near Kabul on 28 September.
Two US helicopters were forced
Most of the other attacks have been claimed by the Taliban, whose government was ousted by a US-led offensive at the end of 2001.
The US-led coalition has been in Afghanistan since the removal of the Taliban and numbers about 20,000 soldiers, most of them Americans, based mainly in the south and east to hunt down Taliban and other fighters.
Two US Chinook helicopters involved in the operations were forced to make emergency landings in separate locations in southern Afghanistan on Sunday, the US military said. Five American servicemen and an Afghan soldier were injured.
"Both CH-47 aircrafts were involved in combat operations against enemy forces in southern Afghanistan. The causes of the incidents are under investigation," it said in a statement.
The Afghan National Army soldier was hurt during a landing at a forward operating base in Uruzgan province, the US military said.
The five US soldiers were hurt in a hard landing north of Kandahar that severely damaged the aircraft.
The five, who were not seriously hurt, were evacuated to a nearby US medical facility for treatment and were in a stable condition, the statement said.
US and Nato troops make up the
ISAF presence in Afghanistan
Muhammad Hanif, a spokesman for the ousted Taliban who is based in Islamabad, Pakistan, said the group had shot down the US helicopter near Kandahar.
Insurgency-linked attacks have undermined Afghanistan's moves towards democracy since the fall of the Taliban, the latest step being successful parliamentary elections in September.
The violence has killed about 1500 people this year, many of them fighters killed in clashes with troops.
While the US-led force has been in eastern and southern Afghanistan, the Nato-led International Security Assistance Force (ISAF) is deployed mainly in the less volatile north and west and in Kabul.